Digital inclusive finance & the high-quality agricultural development: Prevalence of regional heterogeneity in rural China

Developing digital inclusive finance is one of the most effective ways to alleviate financial exclusion in the agriculture sector. For empirical investigation, data from 30 provinces of Rural China is collected from the period 2011 to 2020. The study constructs five dimensions and 22 indicators in total to critically conduct the impact of digital inclusive finance on high-quality agricultural development. The level of agricultural development is measured by entropy weight TOPSIS, and the impact of digital inclusive finance on its high-quality development is empirically tested. The results show that digital inclusive finance has significantly improved the agricultural sector and, particularly, the Eastern region of China has the greatest impact. Three dimensions of digital inclusion finance have regional heterogeneity in terms of impact on agricultural development in Rural China. Data does not show the simple linear relationship between digital inclusion finance and agricultural development quality. The impact of the former on the latter is characterized by the double thresholds. The digital inclusive finance index is the weakest when it is lower than the first threshold that is 4.7704, and the impact of the second threshold that is 5.3186 on high-quality agricultural development is gradually enhanced. After crossing the second threshold, the impact of digital inclusive finance on high-quality agricultural development in Rural China is significantly enhanced. The development of digital inclusive finance should be strengthened in the Central and Western regions to compensate for regional financial imbalances and promote synergy in the high-quality development of agriculture across the country.


Introduction
Since the agricultural reforms and extension, China's agricultural economy has achieved leapfrog development under favorable production environment and efficiency. For instance, grain production has raised from 310 million tons in 1978 to 670 million tons in 2020, an increase of 2.2 times [1], and the output of agro related products such as meat, eggs, vegetables and fish have steadily ranked first in the world. Although China's overall agricultural production capacity has improved significantly in the last few decades, but it is still far away from becoming a world's agricultural power. Domestically, China's agricultural production faces problems such 3. Is there regional heterogeneity in the impact of DIF on the agricultural sector in Eastern, Central and Western China?
4. Is there a threshold effect on the impact of DIF on high-quality agricultural development?

Literature review
Agriculture has attained the pivotal position in the global economy, which not only plays a significant role in the stability of the economies but also improves the livelihood of the people, particularly, of rural areas. In this era of digitalization and information technology, agriculture has begun to adopt the technological tools to achieve convenience, high quality development, productivity and efficiency.
There are a few research works [12][13][14] that analyzed the impact of DIF on high-quality agricultural development, and the research outcomes, especially for the China, are worth referencing. Most of the studies inferred that DIF plays a core role in the availability of funds to rural areas and provides financial support to farmers to develop agricultural modernization and industrialization. Similarly, W. Wang et al. (2022) [9], illustrated the positive relationship between DIF and economic growth and innovative development. Although this empirical study has regional heterogeneity, but still it provides a reference for the role of inclusive finance on agricultural productivity, high-quality, and economic productivity and sustainability. The study was based upon the panel data of 31 provinces of China from 2011 to 2018.
Yu et al. [15] studied the impact of China's inclusive finance on the development of the rural economy. It presented the argument that financial services to rural areas helped to improve the availability of funds to farmers for agricultural development. It is further studied that inclusive finance can trigger the problem of insufficient financial support for modern agricultural development caused by the unavailability of financial services, information, and limited quota. Limitations of capital supply to small farmers are behind the backwardness and unproductivity of the agricultural sector, which can be served effectively by focusing on inclusive finance in rural areas [16].
Zhang [17] conducted the study to highlight the role of DIF in promoting agricultural development. The study introduced the term of "intelligent agriculture," which is attained with access to market information, sufficient financial sources, and human resource accumulation. Zhao et al. [18] highlighted that DIF restructured agricultural activities and fostered the process of agricultural development in agricultural countries, which has narrowed the urban-rural income gap. Su & Chen [19] conducted the empirical investigation of the role of DIF in the development of the agricultural industry. The study consisted of a sample of 31 provinces of China from 2011 to 2019. The study inferred that the reduced information asymmetry, financial cost and difficulty, and educational illiteracy ensure the high-quality agricultural development, farmers' productivity, and the establishment of agricultural industries and enterprises.
It is also studied that traditional inclusive finance has also encountered many practical problems in serving agriculture sector, rural areas and farmers. Zhu et al. [20] described that the traditional financial services to agriculture sector are characterized by small amounts, short-term financing, fragmentation, and mismatch of agricultural production cycle. Relying on the traditional inclusive financial services are not benefitting this sector for technological upgradation, high production and optimum utilization of resources. With the easy access to the internet services in rural areas, the emergence of DIF is considered to be a new way to upgrade and industrialize the agriculture sector [21][22][23].
In the process of supporting agricultural and rural development, DIF has introduced some innovative and result-oriented models. McIntosh & Mansini and Shamin et al. [24,25] studied the practices of different financial supply entities in serving agricultural and rural development; these practices are divided into three types: digital financial services offered by different financial institutions, agricultural supply chain finance with agricultural leading enterprises, and financial product innovation with e-commerce and Fintech companies. To safeguard the interest of beneficiaries, here farmers and agricultural enterprises, the combination of Blockchain and traditional banking services can play a significant role for the business openness, innovation process and transparency of the financial transactions [26].
According to study of [27], the DIF developed a strong rural financial ecological environment by integrating rural commercial activities. This study empirically investigated the provinces having high rural industry integration and concluded that the DIF ultimately improved their level of mechanization in agricultural production, labour productivity, and per unit output with the integration of the financial services, industrialization and access to the international markets. In summary, it can be found that DIF has an important impact on agricultural development as it alleviates the credit constraints, optimizes industrial structure and improves agricultural productivity. Accordingly, this paper puts forward the following hypotheses.
Hypothesis 1: Digital Inclusive Finance promotes high-quality agricultural development particularly in case of Rural China.
Hypothesis 2: All three components of Digital Inclusive Finance significantly contribute high-quality agricultural development in Rural China.
Xie et al. [28] studied that the DIF has the feature of heterogeneity because it influences the agricultural development with multiple supporting factors like demography, adaptability, human capital accumulation and infrastructure. Li et al. [13] conducted the study on China and concluded that the agricultural productivity in most of its rural provinces varies because of different exogenous variables. Some of these core factors are environmental conditions, infrastructure, exposure to the availability of services and resources of each region. Accordingly, this paper puts forward the following hypotheses. Hypothesis 3: There is the regional heterogeneity in determining the impact of Digital Inclusive Finance on high-quality agricultural development in rural areas of China.
Some scholars investigated that whether the relationship between financial development and agricultural development is a simple linear or a threshold effect. Yiting [29] highlighted that the promotion effect of financial development on agricultural development has a threshold characteristic, and this effect increases with the raise in the per capita disposable income of the rural people. Xia et al. [4] used empirical analysis from the perspective of rural economic development and farmers' income to conclude that the role of rural financial development on rural development has time-varying characteristics. Chang [30] used the threshold effect model to illustrate the role of DIF in improving the agricultural productivity and retaining the ecosystem in rural areas of China. From various empirical studies, it is cleared that there is a threshold effect of DIF on high-quality agricultural development. Hence, we propose the following hypothesis Hypothesis 4: The impact of Digital Inclusive Finance on high-quality agricultural development has a threshold effect.
Previous literature mainly focuses on the relationship between Inclusive Finance and agricultural development. With the increase in the accessibility of Internet technology in rural areas, studies [12,29,31] that empirically investigated the impact of new financial format i.e. DIF on agriculture sector. The existing literature is worth learning from, but there are still some research gaps and limitations which can be overcome through changing the estimating methods. First of all, generally the studies were conducted to analysis the impact of DIF on a single factor of agricultural development with limited scope of empirical data, particularly, in case of China. But from the perspective of agricultural high-quality development, research can be conducted more effectively if the focus is on empirical investigation of the level of agricultural development, and comprehensively measure the impact of DIF on agricultural development. Secondly, due to certain differences among the economies, histories and regions, DIF may have different levels or thresholds for high-quality agricultural development [32]. So, the existence of "digital divide" may has a negative effect on agricultural development, and it is necessary to incorporate the threshold effect in the research discussions and analyses. As single element in agricultural development cannot summarize the overall agricultural development, nor it can be effective to determine the role of DIF in influencing the overall agricultural development. This paper is intended to evaluate the status of high quality agricultural development from multiple dimensions and refer to the suitable model to analyze the impact of DIF on the level of high quality agricultural development from an empirical perspective, which to a certain extent enriches the theory of the impact of financial supply on agricultural development. In fact, it fills the research gap of the impact of DIF on the comprehensive development level of the agriculture sector.

Indicator system for measuring quality agricultural development
High-quality agricultural development is labelled as "AGDQ". Subsequent table exhibits the measurement of high-quality agricultural development in the case of rural China. High-quality agricultural development contains five broad dimensions that are further classified into twenty-two (22) variables. See Table 1 for details.
The five dimensions selected for this study are described here. The conditions of agricultural production are directly related to crop yields, which are central to the measurement of agricultural development. Agricultural science and technology support can reflect to some extent the technological progress of agriculture, which is an indispensable support part of the agricultural modernization process. The level of agricultural industrialization represents the rationality of the agricultural industrial structure, and the more rational the industrial structure, the higher the level of agricultural development. Agricultural output efficiency is an important indicator of the quality development of agriculture, and the higher the output efficiency, the higher the level of agricultural development to a large extent. The level of green development in agriculture reflects the health of the agricultural economy and is an important indicator of agricultural sustainable development in the pursue of high-quality development [33].

Measurement methods
This paper adopted a comprehensive evaluation approach to measure the high-quality development of Chinese agriculture sector. This paper selected the period 2011-2020 in which the true spirit of DIF and development period was observed in rural China. Data sources and description of indicators are given in Table 1. The entropy-weighted TOPSIS method can effectively avoid the influence of subjective factors in the process of assigning indicators, and has the advantages of simple calculation process and reasonable measurement output of both the entropy-weighted and TOPSIS methods [33]. Therefore, in order to objectively and reasonably estimate the level of high-quality development of agriculture in each province, this paper adopted the entropy-weighted TOPSIS method for measurement and evaluation, with the following equations: (1) Data standardization processing (2) Calculate the proportion P of index J in the ith year (4) Calculate the redundancy of the information entropy of the jth index ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi The projected sample population is socially deprived people belong to the rural areas of China. In today's globalized world, mainly rural population has limited exposure to the modern technology and resources. Similarly, as habitually, rural masses rely greatly on traditional inclusive finance, which has its own drawbacks, limitations and inefficiencies. Hence, there is a need to introduce DIF in such areas to promote digitalization, uplift high-quality agricultural development and rural revitalization. For empirical evidence, researchers used two-stage least squares (2SLS), robustness regression and threshold modeling. Primarily, this research has been grounded in the following model:

Model descriptions
This model focuses mainly on LDIF and high-quality agricultural development (AGDQ). However, this research utilizes some control variables which are LCPI, LECNDQ, LINDS, RHMC, URB, GOVT, LDOP, and LDI. The observed DIF index is built on three major components: LBRC, LDDIG, and LDUSE. Therefore, it is necessary to incorporate the impact of these three components separately. Hence, in the 2 nd model of this research, the impact of LBRC on AGDQ has been examined. This model is given below.
In the third model, researchers examined the degree of digitalization (LDDIG) and highquality agricultural development (AGDQ). This model is as follows: Furthermore, in the last and 4 th econometric model, the examiner considered the impact of LDDIG on AGDQ.
This model is given below.
The abbreviated terms occupied above displays; AGDQ = high-quality agricultural development LDIF = Log of digital inclusive finance index LBRC = Log of breadth of coverage LDDIG = Log of degree of digitalization LDUSE = Log of depth of use LCPI = Inflation LECNDQ = log of economic development level (gross regional per-capita income) LINDS = Log of industrial structure URB = level of Urbanization (urban population/resident population) RHMC = rural human capital accumulation GOVT = govt. intervention (expenses on agri., forestry, & water affairs/regional GDP) LDOP = Log of Degree of regional openness LDI = Log of Disposable income ε = Error term Moreover, β 0 reflects constant or intercept term. However, β 0 , β 2 , β 3 , β 4 , β 5 , β 6 , β 7 , β 8 , β 9 specifies coefficients which determine the impact of explanatory variables over response variable. Here, "t" reflects the time frame over the period i.e. 2011-2020 while, "i" term denotes cross sections or the selected 30 provinces of China.
Digital Inclusion Finance (LDIF) Index has been published by Peking University's Digital Finance Research Centre that examines nine phases of DIF that are coverage, payments, insurance, depth of use, money funds, credit, investment, credit research, and digitalization. This index is the most illustrative indicator of the extent of DIF development in rural China. It is also extensively utilized by Chinese researchers. In this research, data is collected based on three broad dimensions: breadth of coverage, the depth of usage, and the degree of digitalization. 30 provinces of China are selected because of the availability of data through reliable and credible sources.

Descriptive statistics
Below tables shows the statistical description of the dataset. The advantage of such statistics is to summarize the all observations and present these in an organized way. The key benefit of descriptive statistics is to highlight salient features of the examined data used for the estimation and analysis. Primarily, descriptive statistics include average mean tendencies, maximum and minimum values, standard deviation, skewness, kurtosis, and the actual number of observations [34]. In order to develop descriptive statistics, Eviews-9 software has been used.
Below Table 2 shows the descriptive statistics of the dataset: The largest mean value is of LECND which is 10.8406. Additionally, the largest maximum value is also of LECND, which is approximately 12.0130 units, while the smallest/minimum value is of LDOP, which is approximately 0.0075. Furthermore, as compared to other variables, LBRC possesses the highest standard deviation, which is 0.8201, while the lowest standard deviation is that of inflation (LCPI), which is 0.0113. Here, LDIF, LBRC, LDDIG, and LDUSE are negatively skewed. On the other hand, LCPI, LECND, LINDS, RHMC, URB, GOVT, LDOP, and LDI are positively skewed. As far as normality of data is concerned, all variables are normally distributed towards their respective mean values. In addition, all the research variables in this research are leptokurtic. In the last column of descriptive statistics, the actual number of observations has been displayed, which is 300.
After checking prominent characteristics of the dataset, the next step is to evaluate the inter-correlation between considered variables. For this purpose, correlation matrix is used which is used to determine the degree and nature of association between the variables under consideration. Furthermore, with the help of this, one can easily detect the multi-coordinate presence [35]. In below Table 3, the correlation matrix is shown; Table-3 exhibits the correlation between the dependent and independent variables of this research work. Each variable has a perfect correlation with itself, as demonstrated by diagonal number 1. Consequently, correlation is confirmed with other variables ranges between 0 and In line with the correlation matrix and with the help of causality plotting, cause and effect association between two examined series can be determined. For this purpose, Granger causality is used to determine the causality among the research variables via Eviews software. This estimation can replicate that either the correlation between the variables is bidirectional or linear in nature. In its most basic form, it demonstrates that either 'x' factor causes 'y' or 'y' also causes 'x'. If only 'x' causes an effect on the 'y' factor while 'y' does not cause an effect on 'x', then it can be inferred that the nature of association is linear. But if both factors cause an effect on each other, the association is said bidirectional. A Granger causality table is presented in below Table 4; It is estimated that LDIF and AGDQ have two-ways static effect on each other. Therefore, it is confirmed that there exists a bidirectional relationship between these two variables and this asserts cause and effect association with AGDQ, and AGDQ also asserts cause and effect association with LDOP. In the end, LDI has two-way causality with AGDQ. After analyzing the cause and effect relationship among the variables, the next step is to check the stationarity of the data set for which unit root test is used. Basically, stationary test is performed to detect the presence of unit root in the observations. A data is said to be stationary, only if its mean, variance, and the covariance values remain constant over the flow of time [36]. Below Table 5 shows the result of unit root test; Here, 'Common Unit Root' (presented by Levin, lin, and Chu) and 'Individual Unit Root' (by Im, Pesaran & Shin) tests are used to check the stationarity of the dataset. Here, two grounds are considered: 'level' (differential pre-series) and the 'first difference' (post differential series) to determine the data stationarity. All employed variables of this study affirmed their significance at 1%, and there is no presence of unit root in our dataset. AGDQ, LDIF, LDDIG, LDUSE, LCPI, LINDS, RHMC, GOVT, LDOP, and LDI confirmed their significance at 1% at selected criteria of 1st difference. Though, LBRC, LECNDQ, and URB are significant at level. Except LDUSE, all other variables such as AGDQ, LDIF, LDDIG, LDUSE, LCPI, LINDS, RHMC, GOVT, LDOP, and LDI are significant at 1% pre-differential series. In other words, except LDUSE all other research variables are integrated of order I (0).
Endogenous problems can lead to biased estimation parameters of fixed effect models. In order to diagnose whether there are endogenous problems caused by incorrect model designation, measurement error, missing variables or simultaneity, the Hausman test is used. The Hausman test is also called "Durbin Wu Hausman" (DWH) and endogenous "enhanced regression" test. See below Table 6 for complete results of the Hausman test; It is estimated that the P values of all variables of Hausman test are less than 0.1; therefore, there is no issue of endogenous in the model. When there is no endogenous problem, we can choose OLS for regression analysis or Two-Stage Least Square (2SLS) which is mostly applied for structural equations and an extension of simple OLS test. Here, 2SLS is used when error terms of dependent variable correlates with the independent variable. Furthermore, it examines the 'Local Average Treatment Effect' (LATE) whereas simple OLS determines the 'Average Treatment Effect' (ATE). Hence, it is better to apply 2SLS as it has the same assumptions of OLS regression which are: observations needs to be independent, error term variance for all variables must be the same, error term needs to be normally distributed, and the absence of outliers. The following Table 7 exhibits 2SLS estimations of all four models discussed in this research work.
Models I to IV consider the impact of the total DIF Index, and its breadth of coverage, digitization and depth of use respectively, on high quality development in agriculture. As shown in Table 6, the overall regression results of the model are good with all variables having a significant positive impact on high-quality agricultural development. Among the control variables, rural human capital accumulation as well as disposable income per capita have positive impact on high quality agricultural development. The higher the level of rural human capital accumulation, the stronger its spillover effect, and the more highly intelligent and qualified personnel can play significant role for high-quality agricultural development particularly in case of China. The higher the per capita disposable income in rural areas, the easier it is for farmers to move from the pursuit of "quantity" to the pursuit of "quality".
The estimated results, as given above, can be justifiable with strong arguments. First, efficient rural credit markets and improved banking infrastructure can promote agricultural growth [7]. The development of DIF in rural China can improve the accessibility of financial services. Through advanced digital technology, DIF breaks the spatial and temporal limitations of the traditional financial services and, as a result, more agricultural operators and  Table 7. Results of 2SLS estimation of the impact of digital inclusion finance on high-quality agricultural development.  participants in agricultural development enjoy rural financial services which leads to alleviating the problem of budget constraints caused by insufficient funds and ultimately promote the high-quality agricultural development in many ways. Secondly, under the ecosystem of DIF, living standard of rural areas improves and poverty alleviates. They utilize the financial and non-financial resources in a better way with the easy access to the more business opportunities and markets [12]. Finally, DIF can simultaneously enhance the degree of infrastructure, which provides better basic conditions for the development of digital and technological agriculture, and to a certain extent promotes the agricultural enterprises. Based on the above analysis, H 01 is accepted that is DIF can promote high-quality agricultural development.

Model-1 (LDIF) Model-2 (LBRC) Model-3 (LDDIG) Model-4 (LDUSE
Although economic development improvement (LECND) will have an affirmative effect on high-quality agricultural development (AGDQ), there's a 0.03 change in AGDQ from LECND. Moreover, increase in per-capita level improves the living standards of the rural people, which is one of the driving factors for high-quality agricultural development. However, LINDS asserts a negative effect on AGDQ; there's a 0.01 decline in AGDQ because of LINDS. Improving industrial structure while ignoring agriculture will undoubtedly impede high-quality agricultural development. Besides, RHMC causes a 0.05 increase in AGDQ. The reason behind this affirmative association is that advancement in rural human capital (an increase in the number of educated and skilled labors) stimulates high-quality agricultural development [16]. Additionally, URB has negative relationship with AGDQ; there's a 0.12 decline in AGDQ from one unit increase in the URB. An increased level of urbanization results in less facilitated rural areas, which has a negative influence on high-quality agricultural development. Similarly, GOVT causes a 0.03 decline in AGDQ which means that increased government intervention also hinders the path of high-quality agricultural development. LDOP also asserts a negative effect on AGDQ; it causes a 0.5 decline in AGDQ. LDI has a positive relationship with highquality agricultural development; an increase in the personal incomes of the rural people will improve their living standards, education level, and agricultural technology adoption rate, which in turn raises the chances of attaining high-quality agricultural development [18,37]. At t he end, the R-square value is 0.80, which asserts that the examined model is quite good and well explained.
The results from Models 2, 3 and 4 show that all three dimensions of LDIF contribute positively to AGDQ. Among them, the LDUSE leads to 33.72% change in AGDQ, which has the highest impact among the selected dependent variables; the LBRC has the second highest degree of impact on AGDQ which is about 30.58%; the LDDIG has the relatively smallest impact on AGDQ which is 21.16%. Reason for this phenomenon may be that the LDUSE consists of credit, investment, insurance and fund businesses. For high agricultural production and operational activities, the business entities and enterprises can better invest and allocate the funds through online banking system. This expands the agriculture sector through industrialization, diversification in product portfolio, access to different local and international markets and utilization of idle funds for productive activities. The LDDIG, on the other hand, is in terms of affordability and creditworthiness, suggests that there are still some shortcomings with regard to interest rate bands and credit issues in LDIF.
Despite the different degrees of impact, overall all three dimensions contribute to AGDQ, and the estimation leads to the acceptance of the hypothesis H 02 . For checking the creditability of long run results obtained from 2SLS, there is a need to assimilate the creditability and significance of the results. Hence, for this purpose, robustness regression has been applied. With the help of robustness test, it can be confirmed that the dataset has the reliability, accuracy, and creditability of Table 7 statistics. See below the Table 8 for results; In the subsequent Table 8, robustness in regression estimation has been exhibited for all four models examined in this research. Except for the case of LDUSE, we can conclude from Table 6 that the robustness statistics results are very similar to the 2SLS estimates in Table 5.
Here, LDIF asserts 51% influence on AGDQ while it was 61% in Table 5. However, LBRC asserts the same effect, which is approximately 30%. Besides, LDDIG causes a 20% change according to robustness statistics, while it was 21% in 2SLS estimation. LDUSE asserts a 1%   change here, but it was 33% in accordance with 2SLS estimation. As in Table 5, all variables are statistically significant here, with the exception of LCPI, which is insignificant for models 1 and 2. Consequently, R 2 is 68%, 64%, 64%, and 68% for models-1, model-2, model-3, and model-4, respectively. Next step is to check the hypothesis-3 which is about the regional heterogeneity. For this purpose, 2SLS approach is used for rural China (Eastern, Central, and Western provinces). For further details, see the following Table 9;

Model-1 (LDIF) Model-2 (LBRC) Model-3 (LDDIG) Model-4 (LDUSE
In the Table 9, regional heterogeneity estimation has been represented using 2SLS. Here, model-1 of this research has been tested at regional level. From above statistics, it is shown that LDIF emphasizes 51% change in Eastern region, 35% change in Central region, while 20% change in Western region. It is to be noted that the developed regions incur more significant effect on high-quality agricultural development than that of backward regions. Eastern China that is the utmost developed, dynamic, and advanced region of China has the most favorable result which constructs a stable path for high-quality agricultural development [38]. As far as backward regions are concerned, there is a need to focus on the infrastructure and digitalization of the banking and commercial services in order to equip them for attaining high-quality agricultural development. Followed by Eastern Region, there is Central China which is a developing region. Western region falls in the list of backward provinces of China and has the limited role in high quality agricultural development. About hypothesis-3, the null hypothesis can be rejected which can be inferred that there is the presence of regional heterogeneity. Consequently, R 2 is 66%, 77%, and 82% for case 1, 2, and 3, respectively. Now, next step is to estimate the model-2 and the presence of regional heterogeneity. For this purpose, by using 2SLS approach, rural China (Eastern, Central, and Western provinces) has been tested for empirical examination. For better understanding see the following Table 10. Table 10 presents the regression results of the regional heterogeneity of LBRC, LDDIG and LDUSE respectively. As it can be seen in Tables 9 and 10 that the regression results for LBRC and LDDIG follow the same trend as for the LDIF on AGDQ in Table 8 specifically in terms of the degree of impact. However, the result in Table 10 for the impact of LDUSE on AGDQ, the Eastern region is still the most influential region with a coefficient of 26.21%, followed by the Western region (21.98%) than the Central region (11.03%). There are two possible reasons for this phenomenon: first, the components of LDUSE, and the "inclusive" nature of DIF has a more significant effect on alleviating credit constraints in less developed regions. The Central region is better developed than that of Western region, so its role is not as strong as that of the Western region. The Eastern region, on the other hand, has been the most economically dynamic region in China, and is the best in terms of both acceptance of DIF and the basic conditions for agricultural development. Therefore, the Eastern region continues to have the highest degree of influence on AGDQ in terms of LDUSEI. Secondly, there may be a threshold effect on the impact of LDIF on AGDQ after a certain level is crossed. Here, the threshold characteristics is estimated, based on S. Wang [39] research method, and set up a panel threshold model to investigate its threshold characteristics. Since the exact number of thresholds is not known, a single threshold model is assumed first, and the panel threshold model is set up as follows.
q i represents the threshold variable, ε it is the random error term, and the rest of the symbols indicate the same as above.
In threshold regression, a threshold value or the set of threshold values are used. The purpose behind setting threshold level is to distinguish between ranges of values where the behavior anticipated by model differs in some manners. Threshold regression quantifies accurately how much indication may change (such as potential biases, or the sampling variation) before endorsement changes, and what would be the recommendation for revision. Threshold regression follows the same assumptions as does the least square which are the linear relationship, independence of observations, homoscedasticity, and normal distribution. In addition, hypothesis-4 is tested for detecting threshold effects and determining the required threshold level. For this purpose, the threshold regression approach has been utilized for empirical investigation. For better understanding, see the following Table 11: With the help of Table 11, the study tries to explicate the statistical estimates obtained from threshold effect testing. In this paper, the index of DIF has been taken as a threshold variable.
LDIF has been tested against three threshold levels. As shown in the above table, significance has been checked at 10%, 5%, and 1% levels. As we see, a single threshold value is statistically significant at a confidence level of 1%, while a double threshold value is statistically significant at a confidence level of 5%. However, the triple threshold value did not pass the statistical significance criteria and it is insignificant. This shows that the effect of DIF does not have a simple linear relationship with high-quality agricultural development and, hence, there exist double threshold characteristics. This validates the acceptance of alternative hypothesis 4, and the rejection of the null hypothesis. Therefore, threshold regression estimation is made and given in below Table 12: Above result shows that there is positive and statistically significant threshold effect of the DIF index on high-quality agricultural development. Besides, all of the variables have significantly passed the significance criteria at 1% level. The values of 4.7704, between 4.7704 and 5.3186, and higher than 5.6442 are regarded as low, medium, and high threshold levels, respectively. In particular, when LDIF is not higher than 4.7704, and one unit change in DIF causes the change of 0.5540 unit in high-quality development of agriculture. When LDIF is between 4.7704 and 5.3186, the role of DIF in promoting high-quality agricultural development is more static and significant. Here, high-quality agricultural development increases by 0.6122 units on an average. Additionally, when LDIF is higher than 5.6442, the role of DIF in promoting highquality agricultural development is further increased, and coefficient impact reaches 0.8011 units.
The above statistics show that by improving the DIF the high-quality agricultural development significantly increased particularly in China. According to threshold regression estimation, all variables except RHMC and LDOP confirmed their statistical significance at 1% level. Here, R 2 value is 93%, which confirms the goodness of fit or statistical creditability of the model. On the basis of Hypothesis-4, we can reject the null hypothesis and validate the presence of a threshold effect.

Conclusions and policy implications
This study uses data on rural China from 2011-2020 and selects 22 indicators to construct a system for high-quality agricultural development. The entropy-weighted TOPSIS method was applied to comprehensively evaluate the level of high-quality development of Chinese agriculture. The relationship between the explanatory and response variables are subsequently analyzed through empirical tests. It was found that: firstly, DIF along with LBRC, LDDIG and LDUSE have significant contribute to the level of agricultural quality development. Secondly, there is regional heterogeneity in the effect of DIF on AGDQ, except of LDUSE which is the weakest in the case of Central region and similarly in case of East and West China. The strength of other two dimensions i.e. LBRC and LDDIG and the effect of LDIF on AGDQ show a decreasing trend in case of East, Central and West China. Finally, the results of the threshold effect model show that the relationship between DIF and AGDQ is not the linear one, and that the former has a double threshold characteristic on the latter. This shows that there is a causal relationship between the uneven development of high-quality agriculture across China and the uneven development of DIF. Based on the above findings, following recommendations can be made.
1. Strengthen the development of DIF to promote high-quality agricultural development [40]. Firstly, the government should provide policy support and guide social capital injection into rural areas to put the policy dividends into practice. Secondly, infrastructure should be given priority which includes the electronic terminals, internet lines and other related infrastructure. Finally, financial institutions should actively promote and develop set-up for DIF knowledge to enhance the financial literacy of rural residents and promote their acceptance of IT-enabled financial services.
2. Focus of DIF development should be given to the less developed regions of the China to alleviate the regional imbalance and improve their role for high-quality agricultural development. Due economic opportunities, infrastructure, resource endowment and planting differences among regions have led to obvious regional heterogeneity. Support for lagging regions should be strengthened; DIF development should be promoted based on realistic conditions, and innovative DIF products should be offered to support the development of agricultural technology, talent, large-scale operations and specialized operations. Avoid the emergence of the horse-trust effect causing the differences between East and West parts of China.
3. Construct DIF development strategies in a comprehensive and multi-faceted manner, and adhere to the principle of appropriateness to promote the same in the rural areas of the China. The research results show that the impact of the level of DIF development on the high-quality development of agriculture has threshold characteristics, and when the second threshold is exceeded, the this effect is significantly enhanced. For regions where the LDIF index is below the second threshold, strategies to enhance DIF development should be formulated according to the local conditions, and for regions above the second threshold, DIF development should continue to be strengthened in order to facilitate stronger promotion of high-quality agricultural development.

Limitations
The study has a number of limitations that could be considered for future research. Firstly, our study is based on the analysis of data measured by the Centre of Peking University. The data is collected from Ant Financial Services, which is highly recognized institute for providing reliable data but this is a single source of data collection and the study could not considered the data from the other financial institutions in China. Future empirical analysis can be conducted by collecting data on DIF related businesses from formal and informal financial institutions of China. Secondly, although the researchers have tried to measure the level of quality development of agriculture from different dimensions and indicators to measure its development, but still it is not enough and we hope that future studies can be conducted by measuring the agriculture development in more precise way. Finally, it is encouraged to analyze the regression of the three dimensions of DIF in more depth, such as how the credit, fund, investment and insurance businesses included in LDUSE affect the high quality development of agriculture, and what is the significance of the affordability and facilitation of LDDIG in this regards.